S.1: Number Sense, Properties, and Operations

S.1.GLE.1: In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line

S.1.GLE.1.RA: Relevance and Application:

S.1.GLE.1.RA.1: Irrational numbers have applications in geometry such as the length of a diagonal of a one by one square, the height of an equilateral triangle, or the area of a circle.

Circumference and Area of Circles

S.1.GLE.1.RA.3: Technologies such as calculators and computers enable people to order and convert easily among fractions, decimals, and percents.

Percents, Fractions, and Decimals

S.1.GLE.1.N: Nature of Mathematics:

S.1.GLE.1.N.2: Mathematicians reason abstractly and quantitatively.

Biconditional Statements
Conditional Statements

S.2: Patterns, Functions, and Algebraic Structures

S.2.GLE.1: Linear functions model situations with a constant rate of change and can be represented numerically, algebraically, and graphically

S.2.GLE.1.RA: Relevance and Application:

S.2.GLE.1.RA.2: Understanding slope as rate of change allows individuals to develop and use a line of best fit for data that appears to be linearly related.

Solving Using Trend Lines

S.2.GLE.1.RA.3: The ability to recognize slope and y-intercept of a linear function facilitates graphing the function or writing an equation that describes the function.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

S.2.GLE.1.N: Nature of Mathematics:

S.2.GLE.1.N.1: Mathematicians represent functions in multiple ways to gain insights into the relationships they model.

Function Machines 1 (Functions and Tables)
Introduction to Functions

S.2.GLE.1.N.2: Mathematicians model with mathematics.

Estimating Population Size

S.2.GLE.2: Properties of algebra and equality are used to solve linear equations and systems of equations

S.2.GLE.2.IQ: Inquiry Questions:

S.2.GLE.2.IQ.1: What makes a solution strategy both efficient and effective?

Estimating Population Size

S.2.GLE.2.RA: Relevance and Application:

S.2.GLE.2.RA.1: The understanding and use of equations, inequalities, and systems of equations allows for situational analysis and decision-making. For example, it helps people choose cell phone plans, calculate credit card interest and payments, and determine health insurance costs.

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

S.2.GLE.2.RA.2: Recognition of the significance of the point of intersection for two linear equations helps to solve problems involving two linear rates such as determining when two vehicles traveling at constant speeds will be in the same place, when two calling plans cost the same, or the point when profits begin to exceed costs.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side

S.2.GLE.2.N: Nature of Mathematics:

S.2.GLE.2.N.3: Mathematicians make sense of problems and persevere in solving them.

Estimating Population Size

S.2.GLE.3: Graphs, tables and equations can be used to distinguish between linear and nonlinear functions

S.2.GLE.3.IQ: Inquiry Questions:

S.2.GLE.3.IQ.2: Why are patterns and relationships represented in multiple ways?

Linear Functions
Pattern Finder

S.2.GLE.3.IQ.3: What properties of a function make it a linear function?

Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Linear Functions
Slope-Intercept Form of a Line

S.2.GLE.3.RA: Relevance and Application:

S.2.GLE.3.RA.1: Recognition that non-linear situations is a clue to non-constant growth over time helps to understand such concepts as compound interest rates, population growth, appreciations, and depreciation.

Compound Interest

S.3: Data Analysis, Statistics, and Probability

S.3.GLE.1: Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge

S.3.GLE.1.IQ: Inquiry Questions:

S.3.GLE.1.IQ.2: How is it known that an apparent trend is just a coincidence?

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

S.3.GLE.1.IQ.3: How can correct data lead to incorrect conclusions?

Conditional Statements

S.3.GLE.1.RA: Relevance and Application:

S.3.GLE.1.RA.1: The ability to analyze and interpret data helps to distinguish between false relationships such as developing superstitions from seeing two events happen in close succession versus identifying a credible correlation.

Box-and-Whisker Plots
Polling: City
Real-Time Histogram

S.3.GLE.1.RA.2: Data analysis provides the tools to use data to model relationships, make predictions, and determine the reasonableness and limitations of those predictions. For example, predicting whether staying up late affects grades, or the relationships between education and income, between income and energy consumption, or between the unemployment rate and GDP.

Polling: City

S.3.GLE.1.N: Nature of Mathematics:

S.3.GLE.1.N.2: Mathematicians construct viable arguments and critique the reasoning of others.

Biconditional Statements

S.3.GLE.1.N.3: Mathematicians model with mathematics.

Estimating Population Size

S.4: Shape, Dimension, and Geometric Relationships

S.4.GLE.1: Transformations of objects can be used to define the concepts of congruence and similarity

S.4.GLE.1.IQ: Inquiry Questions:

S.4.GLE.1.IQ.2: How can you physically verify that two lines are really parallel?

Parallel, Intersecting, and Skew Lines

S.4.GLE.1.RA: Relevance and Application:

S.4.GLE.1.RA.1: Dilations are used to enlarge or shrink pictures.

Dilations
Similar Figures

S.4.GLE.1.N: Nature of Mathematics:

S.4.GLE.1.N.2: Mathematicians construct viable arguments and critique the reasoning of others.

Biconditional Statements

S.4.GLE.1.N.3: Mathematicians model with mathematics.

Estimating Population Size

S.4.GLE.2: Direct and indirect measurement can be used to describe and make comparisons

S.4.GLE.2.IQ: Inquiry Questions:

S.4.GLE.2.IQ.1: Why does the Pythagorean Theorem only apply to right triangles?

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

S.4.GLE.2.IQ.2: How can the Pythagorean Theorem be used for indirect measurement?

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

S.4.GLE.2.IQ.3: How are the distance formula and the Pythagorean theorem the same? Different?

Circles
Distance Formula

S.4.GLE.2.IQ.4: How are the volume formulas for cones, cylinders, prisms and pyramids interrelated?

Prisms and Cylinders
Pyramids and Cones

S.4.GLE.2.RA: Relevance and Application:

S.4.GLE.2.RA.1: The understanding of indirect measurement strategies allows measurement of features in the immediate environment such as playground structures, flagpoles, and buildings.

Estimating Population Size
Similar Figures

S.4.GLE.2.RA.2: Knowledge of how to use right triangles and the Pythagorean Theorem enables design and construction of such structures as a properly pitched roof, handicap ramps to meet code, structurally stable bridges, and roads.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

S.4.GLE.2.RA.3: The ability to find volume helps to answer important questions such as how to minimize waste by redesigning packaging or maximizing volume by using a circular base.

Prisms and Cylinders

S.4.GLE.2.N: Nature of Mathematics:

S.4.GLE.2.N.3: Mathematicians make sense of problems and persevere in solving them.

Estimating Population Size

S.4.GLE.2.N.4: Mathematicians construct viable arguments and critique the reasoning of others.

Biconditional Statements